This calculator solves the Pythagorean Theorem equation for sides a or b, or the hypotenuse c. The hypotenuse is the side of the triangle opposite the right angle. In terms of the right triangle in Fig. 6.11, the lefthand side of the first inequality in Eq. (6.37) is the square of the hypotenuse, and the righthand side is the square of the leg (from the Pythagorean theorem usage in Eq. (6.35)). Pythagoras. Over 2000 years ago there was an amazing discovery about triangles: When a triangle has a right angle (90°). Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points. Pythagorean Theorem calculator to find out the unknown length of a right triangle. It can provide the calculation steps, area, perimeter, height, and angles. Thus, the Pythagorean Theorem states that the area of the square formed by the longest side of the right triangle (the hypotenuse) is equal to the sum of the area of the squares formed by the other two sides. The Pythagorean theorem describes how the three sides of a right triangle are related. It states that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse. How to use the pythagorean theorem, explained with examples, practice problems, a video tutorial and pictures. Definition of Pythagorean Theorem For a given right triangle, it states that the square of the hypotenuse, c c, is equal to the sum of the squares of the legs, a a and b b.